Subgroups — C₂×C₅²×Q₈ #87909

Order 400.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×Q₈	C₂	1	4	yes	maximal, direct product factor
2	C₂×C₄×C₅²	C₂	1	3	yes	maximal
3	C₂²×C₅²	C₂²	1	1	yes	characteristic
4	C₄×C₅²	C₂²	1	6	yes	—
5	C₂×C₅×Q₈	C₅	1	6	yes	maximal, direct product factor
6	C₂×C₅²	Q₈	1	2	yes	direct product factor
7	C₂×C₅²	C₂³	1	1	yes	characteristic
8	C₅×Q₈	C₂×C₅	1	24	yes	direct product factor
9	C₂×C₄×C₅	C₂×C₅	1	18	yes	—
10	C₅²	C₂×Q₈	1	1	yes	characteristic, direct product factor, Sylow
11	C₂²×C₅	C₂²×C₅	1	6	yes	—
12	C₄×C₅	C₂²×C₅	1	36	yes	—
13	C₂×Q₈	C₅²	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₅	C₅×Q₈	1	12	yes	direct product factor
15	C₂×C₅	C₂³×C₅	1	6	yes	—
16	Q₈	C₂×C₅²	1	4	yes	direct product factor
17	C₂×C₄	C₂×C₅²	1	3	yes	—
18	C₅	C₂×C₅×Q₈	1	6	yes	direct product factor
19	C₂²	C₂²×C₅²	1	1	yes	characteristic
20	C₄	C₂²×C₅²	1	6	yes	—
21	C₂	C₅²×Q₈	1	2	yes	direct product factor
22	C₂	C₂³×C₅²	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₅²	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₅²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅² ◁ G

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.